Question

4x - 3y = 5\\-4x + 2y = 2

Explanation:

Step1: Label the equations

Let:
$4x - 3y = 5$ --- (1)
$-4x + 2y = 2$ --- (2)

Step2: Eliminate $x$ by adding equations

Add (1) and (2):
$(4x - 3y) + (-4x + 2y) = 5 + 2$
$4x - 4x - 3y + 2y = 7$
$-y = 7$

Step3: Solve for $y$

Multiply both sides by $-1$:
$y = -7$

Step4: Substitute $y=-7$ into (1)

$4x - 3(-7) = 5$
$4x + 21 = 5$

Step5: Solve for $x$

Subtract 21 from both sides:
$4x = 5 - 21$
$4x = -16$
Divide by 4:
$x = \frac{-16}{4} = -4$

Answer:

$x=-4$, $y=-7$